/export/starexec/sandbox2/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES

Problem:
 app(id(),x) -> x
 app(add(),0()) -> id()
 app(app(add(),app(s(),x)),y) -> app(s(),app(app(add(),x),y))
 app(app(map(),f),nil()) -> nil()
 app(app(map(),f),app(app(cons(),x),xs)) -> app(app(cons(),app(f,x)),app(app(map(),f),xs))

Proof:
 Extended Uncurrying Processor:
  application symbol: app
  symbol table:
   cons ==> cons0/0 cons1/1 cons2/2
   nil ==> nil0/0
   map ==> map0/0 map1/1 map2/2
   s ==> s0/0 s1/1
   0 ==> 00/0
   add ==> add0/0 add1/1 add2/2
   id ==> id0/0 id1/1
   
  uncurry-rules:
   app(id0(),x5) -> id1(x5)
   app(add1(x7),x8) -> add2(x7,x8)
   app(add0(),x7) -> add1(x7)
   app(s0(),x11) -> s1(x11)
   app(map1(x13),x14) -> map2(x13,x14)
   app(map0(),x13) -> map1(x13)
   app(cons1(x17),x18) -> cons2(x17,x18)
   app(cons0(),x17) -> cons1(x17)
  eta-rules:
   app(app(add(),0()),x4) -> app(id(),x4)
  problem:
   id1(x) -> x
   add1(00()) -> id0()
   add2(s1(x),y) -> s1(add2(x,y))
   map2(f,nil0()) -> nil0()
   map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
   add2(00(),x4) -> id1(x4)
   app(id0(),x5) -> id1(x5)
   app(add1(x7),x8) -> add2(x7,x8)
   app(add0(),x7) -> add1(x7)
   app(s0(),x11) -> s1(x11)
   app(map1(x13),x14) -> map2(x13,x14)
   app(map0(),x13) -> map1(x13)
   app(cons1(x17),x18) -> cons2(x17,x18)
   app(cons0(),x17) -> cons1(x17)
  DP Processor:
   DPs:
    add{2,#}(s1(x),y) -> add{2,#}(x,y)
    map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
    map{2,#}(f,cons2(x,xs)) -> app#(f,x)
    add{2,#}(00(),x4) -> id{1,#}(x4)
    app#(id0(),x5) -> id{1,#}(x5)
    app#(add1(x7),x8) -> add{2,#}(x7,x8)
    app#(add0(),x7) -> add{1,#}(x7)
    app#(map1(x13),x14) -> map{2,#}(x13,x14)
   TRS:
    id1(x) -> x
    add1(00()) -> id0()
    add2(s1(x),y) -> s1(add2(x,y))
    map2(f,nil0()) -> nil0()
    map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
    add2(00(),x4) -> id1(x4)
    app(id0(),x5) -> id1(x5)
    app(add1(x7),x8) -> add2(x7,x8)
    app(add0(),x7) -> add1(x7)
    app(s0(),x11) -> s1(x11)
    app(map1(x13),x14) -> map2(x13,x14)
    app(map0(),x13) -> map1(x13)
    app(cons1(x17),x18) -> cons2(x17,x18)
    app(cons0(),x17) -> cons1(x17)
   TDG Processor:
    DPs:
     add{2,#}(s1(x),y) -> add{2,#}(x,y)
     map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x)
     add{2,#}(00(),x4) -> id{1,#}(x4)
     app#(id0(),x5) -> id{1,#}(x5)
     app#(add1(x7),x8) -> add{2,#}(x7,x8)
     app#(add0(),x7) -> add{1,#}(x7)
     app#(map1(x13),x14) -> map{2,#}(x13,x14)
    TRS:
     id1(x) -> x
     add1(00()) -> id0()
     add2(s1(x),y) -> s1(add2(x,y))
     map2(f,nil0()) -> nil0()
     map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
     add2(00(),x4) -> id1(x4)
     app(id0(),x5) -> id1(x5)
     app(add1(x7),x8) -> add2(x7,x8)
     app(add0(),x7) -> add1(x7)
     app(s0(),x11) -> s1(x11)
     app(map1(x13),x14) -> map2(x13,x14)
     app(map0(),x13) -> map1(x13)
     app(cons1(x17),x18) -> cons2(x17,x18)
     app(cons0(),x17) -> cons1(x17)
    graph:
     app#(map1(x13),x14) -> map{2,#}(x13,x14) ->
     map{2,#}(f,cons2(x,xs)) -> app#(f,x)
     app#(map1(x13),x14) -> map{2,#}(x13,x14) ->
     map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
     app#(add1(x7),x8) -> add{2,#}(x7,x8) ->
     add{2,#}(00(),x4) -> id{1,#}(x4)
     app#(add1(x7),x8) -> add{2,#}(x7,x8) ->
     add{2,#}(s1(x),y) -> add{2,#}(x,y)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(map1(x13),x14) -> map{2,#}(x13,x14)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(add0(),x7) -> add{1,#}(x7)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(add1(x7),x8) -> add{2,#}(x7,x8)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(id0(),x5) -> id{1,#}(x5)
     map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs) ->
     map{2,#}(f,cons2(x,xs)) -> app#(f,x)
     map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs) ->
     map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
     add{2,#}(s1(x),y) -> add{2,#}(x,y) ->
     add{2,#}(00(),x4) -> id{1,#}(x4)
     add{2,#}(s1(x),y) -> add{2,#}(x,y) -> add{2,#}(s1(x),y) -> add{2,#}(x,y)
    SCC Processor:
     #sccs: 2
     #rules: 4
     #arcs: 12/64
     DPs:
      app#(map1(x13),x14) -> map{2,#}(x13,x14)
      map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
      map{2,#}(f,cons2(x,xs)) -> app#(f,x)
     TRS:
      id1(x) -> x
      add1(00()) -> id0()
      add2(s1(x),y) -> s1(add2(x,y))
      map2(f,nil0()) -> nil0()
      map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
      add2(00(),x4) -> id1(x4)
      app(id0(),x5) -> id1(x5)
      app(add1(x7),x8) -> add2(x7,x8)
      app(add0(),x7) -> add1(x7)
      app(s0(),x11) -> s1(x11)
      app(map1(x13),x14) -> map2(x13,x14)
      app(map0(),x13) -> map1(x13)
      app(cons1(x17),x18) -> cons2(x17,x18)
      app(cons0(),x17) -> cons1(x17)
     Subterm Criterion Processor:
      simple projection:
       pi(map{2,#}) = 0
       pi(app#) = 0
      problem:
       DPs:
        map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
        map{2,#}(f,cons2(x,xs)) -> app#(f,x)
       TRS:
        id1(x) -> x
        add1(00()) -> id0()
        add2(s1(x),y) -> s1(add2(x,y))
        map2(f,nil0()) -> nil0()
        map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
        add2(00(),x4) -> id1(x4)
        app(id0(),x5) -> id1(x5)
        app(add1(x7),x8) -> add2(x7,x8)
        app(add0(),x7) -> add1(x7)
        app(s0(),x11) -> s1(x11)
        app(map1(x13),x14) -> map2(x13,x14)
        app(map0(),x13) -> map1(x13)
        app(cons1(x17),x18) -> cons2(x17,x18)
        app(cons0(),x17) -> cons1(x17)
      SCC Processor:
       #sccs: 1
       #rules: 1
       #arcs: 5/4
       DPs:
        map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
       TRS:
        id1(x) -> x
        add1(00()) -> id0()
        add2(s1(x),y) -> s1(add2(x,y))
        map2(f,nil0()) -> nil0()
        map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
        add2(00(),x4) -> id1(x4)
        app(id0(),x5) -> id1(x5)
        app(add1(x7),x8) -> add2(x7,x8)
        app(add0(),x7) -> add1(x7)
        app(s0(),x11) -> s1(x11)
        app(map1(x13),x14) -> map2(x13,x14)
        app(map0(),x13) -> map1(x13)
        app(cons1(x17),x18) -> cons2(x17,x18)
        app(cons0(),x17) -> cons1(x17)
       Subterm Criterion Processor:
        simple projection:
         pi(map{2,#}) = 1
        problem:
         DPs:
          
         TRS:
          id1(x) -> x
          add1(00()) -> id0()
          add2(s1(x),y) -> s1(add2(x,y))
          map2(f,nil0()) -> nil0()
          map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
          add2(00(),x4) -> id1(x4)
          app(id0(),x5) -> id1(x5)
          app(add1(x7),x8) -> add2(x7,x8)
          app(add0(),x7) -> add1(x7)
          app(s0(),x11) -> s1(x11)
          app(map1(x13),x14) -> map2(x13,x14)
          app(map0(),x13) -> map1(x13)
          app(cons1(x17),x18) -> cons2(x17,x18)
          app(cons0(),x17) -> cons1(x17)
        Qed
     
     DPs:
      add{2,#}(s1(x),y) -> add{2,#}(x,y)
     TRS:
      id1(x) -> x
      add1(00()) -> id0()
      add2(s1(x),y) -> s1(add2(x,y))
      map2(f,nil0()) -> nil0()
      map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
      add2(00(),x4) -> id1(x4)
      app(id0(),x5) -> id1(x5)
      app(add1(x7),x8) -> add2(x7,x8)
      app(add0(),x7) -> add1(x7)
      app(s0(),x11) -> s1(x11)
      app(map1(x13),x14) -> map2(x13,x14)
      app(map0(),x13) -> map1(x13)
      app(cons1(x17),x18) -> cons2(x17,x18)
      app(cons0(),x17) -> cons1(x17)
     Subterm Criterion Processor:
      simple projection:
       pi(add{2,#}) = 0
      problem:
       DPs:
        
       TRS:
        id1(x) -> x
        add1(00()) -> id0()
        add2(s1(x),y) -> s1(add2(x,y))
        map2(f,nil0()) -> nil0()
        map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
        add2(00(),x4) -> id1(x4)
        app(id0(),x5) -> id1(x5)
        app(add1(x7),x8) -> add2(x7,x8)
        app(add0(),x7) -> add1(x7)
        app(s0(),x11) -> s1(x11)
        app(map1(x13),x14) -> map2(x13,x14)
        app(map0(),x13) -> map1(x13)
        app(cons1(x17),x18) -> cons2(x17,x18)
        app(cons0(),x17) -> cons1(x17)
      Qed